Continuation strategies to mitigate convergence to low-performing local optima in topology optimization of sound transmission loss

Abstract

Dynamic topology optimization problems often suffer from convergence to low-performing local optima. This typically results in stiff designs that do not exploit dynamical phenomena such as antiresonance and decoupling. To obtain better designs, researchers often repeat their optimizations with different initial guesses. However, such reruns are computationally expensive and the required number is unknown. To quantify this problem, random initial guesses are sampled and tested for different frequencies on two case studies: (1) dynamic compliance minimization of a reinforced cantilever, which exhibits poor optima for driving frequencies below the first natural frequency, and (2) sound transmission loss maximization of a sandwich panel, which additionally sees a strong tendency toward low-performing optima at high frequencies. To address this issue, the study first divides techniques to reduce the needed number of reruns into four categories: global optimization, exclusion, relaxation, and frequency shift methods. For the latter three, continuation strategies are proposed, illustrated, evaluated and compared on the sound transmission loss case, using Monte Carlo sampling to estimate success rates. All strategies show measurable benefits and trade-offs. To support broader applicability, the study concludes with practical guidelines for dealing with convergence to poor local optima in dynamic topology optimization.